Question

If $$(5x + 2y) : (7x + 4y) = 13 : 20$$, find $$x : y$$.

Answer 1

Write as a fraction: $$\frac{5x + 2y}{7x + 4y} = \frac{13}{20}$$

Cross-multiply: $$20(5x + 2y) = 13(7x + 4y)$$

$$100x + 40y = 91x + 52y$$

Group terms: $$100x - 91x = 52y - 40y$$

$$9x = 12y$$

Find $$\frac{x}{y}$$: $$\frac{x}{y} = \frac{12}{9} = \frac{4}{3}$$

Therefore, $$x : y = 4 : 3$$.